Bulletin of Computational Applied Mathematics (Bull CompAMa)
Derivative-free method for bound constrained nonlinear monotone equations and its application in solving steady state reaction-diffusion problems
Octavio Batta, William La Cruz, Gilberto Noguera
We present a derivative-free algorithm for solving bound constrained systems of nonlinear monotone equations. The algorithm generates feasible iterates using in a systematic way the residual as search direction and a suitable step-length closely related to the Barzilai-Borwein choice. A convergence analysis is described. We also present one application in solving problems related with the study of reaction-diffusion processes that can be described by nonlinear partial differential equations of elliptic type. Numerical experiences are included to highlight the efficacy of proposed algorithm.
Keywords: nonlinear equations; derivative-free algorithm; monotone mapping; reaction-diffusion problems.